In this paper we focus on a long-term dynamic analysis of the optimal adaptation/mitigation mix in the presence of a pollution threshold above which adaptation is no longer efficient. We account for accumulation in abatement capital, greenhouse gases, and adaptation capital in order to better capture the arbitrage between abatement and adaptation investments. Pollution damages arise from the emissions due to the country consumption but also from the emissions of the rest of the world (ROW). A pollution threshold is then introduced, above which adaptation is no longer efficient. We obtain that if this threshold is lower than the steady-state level of pollution, there is no way for the modeled economy to avoid it. In particular, such a situation will appear if the ROW's emissions are high. Next step is then to introduce another type of investment allowing for lower ROW pollution ie. emissions eduction abroad through CDM for instance. We obtain that CDM may be a means to avoid a pollution threshold above which adaptation becomes of no use.